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The permutation flowshop problem is a classic machine scheduling problem where n jobs must be processed on a set of m machines disposed in series and where each job must visit all machines in the same order. Many production scheduling problems resemble flowshops and hence it has generated much interest and had a big impact in the field, resulting in literally hundreds of heuristic and metaheuristic methods over the last 60 years. However, most methods proposed for makesan minimisation are not properly compared with existing procedures so currently it is not possible to know which are the most efficient methods for the problem regarding the quality of the solutions obtained and the computational effort required. In this paper, we identify and exhaustively compare the best existing heuristics and metaheuristics so the state-of-the-art regarding approximate procedures for this relevant problem is established.

As the interest of practitioners and researchers in scheduling in a multi-factory environment is growing, there is an increasing need to provide ecient algorithms for this type of decision problems, characterised by simultaneously addressing the assignment of jobs to dierent factories/workshops and their subsequent scheduling.Here we address the so-called distributed permutation owshop scheduling problem, in which a set of jobs has to be scheduled over a number of identical factories, each one with its machines arranged as a owshop. Several heuristics have been designed for this problem, although there is no direct comparison among them. In this paper, we propose a new heuristic which exploits the specic structure of the problem. The computational experience carried out on a well-known testbed shows that the proposed heuristic outperforms existing state-of-the-art heuristics, being able to obtain better upper bounds for more than one quarter of the problems in the testbed.

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